Optimization of Oscillation Damping Modes of a Spatial Double Pendulum: 2. Solution of the Problem and Analysis of the Results

Abstract

This study is a continuation of the article “Optimization of oscillation damping modes of a spatial double pendulum: 1. Formulation of the problem,” in which the problem of the optimal oscillation damping of a double pendulum with hinged noncollinear axes was formulated. Passive damping (viscous friction) is considered separately, and the possibility of additional account of active impacts (collinear control) is also explored. Two optimization criteria are introduced that characterize the efficiency of the damping of system motion: first, the degree of stability is maximized, and then the integral energy-time criterion is minimized. The optimal values of the parameters of the damping variants under consideration are determined by applying both criteria in finding the exact solution of the problem in a linear model. The results obtained are presented as visual graphic illustrations which enable determination of their main qualitative and quantitative features. The conclusions made can be useful in studying the motions of manipulators and various robotic structures.